What is the regret for (d2, s1)? s1 s2 d1 13 6 d2 10 -5 d3 8 7
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![**Regret Calculation Example**
Let's analyze the following table to understand the concept of regret in decision making:
| | s1 | s2 |
|----|----|-----|
| d1 | 13 | 6 |
| d2 | 10 | -5 |
| d3 | 8 | 7 |
**Question: What is the regret for (d2, s1)?**
To determine the regret for a specific decision in a given state, we compare the payoff for that decision with the best possible payoff for that state.
### Steps to Calculate Regret:
1. **Identify the state (s1):**
- The payoffs for s1 are: 13 (d1), 10 (d2), and 8 (d3).
2. **Determine the best payoff in state s1:**
- The highest payoff in s1 is 13 (from d1).
3. **Calculate the regret for (d2, s1):**
- Regret for (d2, s1) = Best payoff in s1 - Payoff for (d2, s1)
- Regret for (d2, s1) = 13 - 10
- Regret for (d2, s1) = 3
So, the regret for (d2, s1) is **3**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa0073c4-6425-40d1-a8ed-c26ddcc2ccc0%2F7acc9be2-cea3-4110-b7d0-2197f03f0a09%2F6z54ivy_processed.jpeg&w=3840&q=75)
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